Question: Simplify the following expression: $z = \dfrac{-3x^2 + 6x + 24}{x + 2} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ z =\dfrac{-3(x^2 - 2x - 8)}{x + 2} $ Then we factor the remaining polynomial: $x^2 {-2}x {-8} $ ${2} {-4} = {-2}$ ${2} \times {-4} = {-8}$ $ (x + {2}) (x {-4}) $ This gives us a factored expression: $\dfrac{-3(x + {2}) (x {-4})}{x + 2}$ We can divide the numerator and denominator by $(x - 2)$ on condition that $x \neq -2$ Therefore $z = -3(x - 4); x \neq -2$